"Angie" wrote in message <email@example.com>... if anyone can help with my initial question: Which integral approximation method (quad, quadgk, etc.) is the best to evaluate this integral in terms of time and least error?
There is no answer for such generic question. It depends. Text book, research papers usually show which method is suitable for which situation.
That's why we have the choice (why bother to implement the non-best methods?)